On-chip optical polarization controller

ABSTRACT

An example optical polarization controller can include a substantially planar substrate and a waveguide unit cell formed on the substantially planar substrate. The waveguide unit cell can include a first out-of-plane waveguide portion and a second out-of-plane waveguide portion coupled to the first out-of-plane waveguide portion. Each of the first and second out-of-plane waveguide portions can respectively include a core material layer arranged between a first optical cladding layer having a first stress-response property and a second optical cladding layer having a second stress-response property. The first and second stress-response properties can be different such that each of the first and second out-of-plane waveguide portions is deflected by a deflection angle.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/768,828, filed on Feb. 25, 2013, entitled “BROADBANDAND TUNABLE ON-CHIP OPTICAL POLARIZATION ROTATOR,” the disclosure ofwhich are expressly incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY FUNDED RESEARCH

This invention was made with Government support under Grant No. 1102246awarded by the National Science Foundation. The Government has certainrights in the invention.

BACKGROUND

One of the major open challenges for high confinement silicon photonicintegrated circuits is to achieve polarization independence. Largepolarization mode dispersion (“PMD”), polarization dependent loss(“PDL”), and polarization dependent wavelength characteristics arecaused by structural birefringence in silicon strip waveguides.Polarization independent photonic integrated circuits may be achieved byusing a silicon waveguide core that is exactly square in shape. Inreality, however, fabrication errors of only a few nanometers wouldresult in significant birefringence. Quantitatively, for example, givena waveguide cross section of 300 nm×300 nm, a variation of ±5 nm inwidth results in a differential group delay of 7 ps over a 5 cm length.Consequently, a 40 Gbps high-speed data stream would be significantlydegraded under such conditions. Furthermore, the waveguide core widthand height fluctuate randomly along the direction of light propagationdue to fabrication tolerances. The random fluctuation varies the groupindex and results in polarization dependent wavelength characteristicsof wavelength filters. Quantitatively, transverse-electric (“TE”) andtransverse-magnetic (“TM”) modes exhibit a 100 GHz difference inresonance frequency in a 10 micrometer radius ring resonator with a 1 nmvariation in waveguide width. Extremely challenging nanometer accuracyis therefore required for silicon strip waveguide devices used inpolarization-independent dense wavelength division multiplexing systems.

To achieve polarization independent photonic integrated circuits,devices and architectures that attempt to rotate and control opticalpolarization have been pursued. These devices and architectures arereferred to as systems with polarization diversity (or polarizationtransparency). These approaches include asymmetric gratings, waveguideswith asymmetric slanted sidewalls, dual core waveguides with asymmetricaxes, waveguides with asymmetric trenches, triple waveguide couplers,and bi-layer slots. Y. Yue et al., “Higher-order-mode assistedsilicon-on-insulator 90 degree polarization rotator,” Optics Express 17,20694-20699 (2009). S.-H. Kim et al., “Single-trench waveguide TE-TMmode converter,” Optics Express 17, 11267-11273 (2009). H. Fukuda etal., “Polarization rotator based on silicon wire waveguides,” OpticsExpress 16, 2628-2635 (2008). N.-N. Feng et al., “Low-loss compact-sizeslotted waveguide polarization rotator and transformer,” Optics Letters32, 2131-2133 (2007). B. M. A. Rahman et al., “Design andCharacterization of Compact Single-Section Passive PolarizationRotator,” Journal of Lightwave Technology 19, 512-(2001). P. Chan etal., “Mode conversion and birefringence adjustment by focused-ion-beametching for slanted rib waveguide walls,” Optics Letters 28, 2109-2111(2003). These approaches to realize polarization rotators in siliconsuffer from several drawbacks. First, these approaches are static, inthe sense that they rotate the polarization by only a fixed amount.Rotation angles vary among approaches and can be as low as 39°,corresponding to TE-TM conversion efficiencies of 40%. In addition,these approaches rely on asymmetric geometries with impedance mismatchesresulting in degradation of insertion loss. Further, these approachesexhibit wavelength dependent loss because they rely on periodicstructures or mode coupling.

SUMMARY

Described herein are broadband and tunable optical polarizationcontrollers (also referred to herein as “polarization rotators”) withlow insertion loss to achieve dynamically controlled polarizationtransparent photonic integrated circuits (“PICs”).

An example optical polarization controller can include a substantiallyplanar substrate and a waveguide unit cell formed on the substantiallyplanar substrate. The waveguide unit cell can include a firstout-of-plane waveguide portion and a second out-of-plane waveguideportion coupled to the first out-of-plane waveguide portion. Each of thefirst and second out-of-plane waveguide portions can respectivelyinclude a core material layer arranged between a first optical claddinglayer having a first stress-response property and a second opticalcladding layer having a second stress-response property. The first andsecond stress-response properties can be different such that each of thefirst and second out-of-plane waveguide portions is deflected by adeflection angle.

Additionally, the first out-of-plane waveguide portion can be deflectedtoward or away from the substantially planar substrate. Additionally,the second out-of-plane waveguide portion can be deflected toward oraway from the substantially planar substrate.

Alternatively or additionally, an angle of optical polarization rotationbetween input and output light can be a function of the deflectionangle.

Optionally, the optical polarization controller can include a pluralityof waveguide unit cells coupled in series and formed on thesubstantially planar substrate. Additionally, an angle of opticalpolarization rotation between input and output light can be a functionof a number of the waveguide unit cells and the deflection angle.Additionally, the optical polarization controller can include one ormore in-plane waveguide portions. For example, each respective in-planewaveguide portion can be connected between two waveguide unit cells.

Alternatively or additionally, the deflection angle of at least one ofthe first and second out-of-plane waveguide portions can be configuredto be adjustable in response to at least one of an electrical,mechanical, thermal and optical excitation. For example, at least one ofthe first and second out-of-plane waveguide portions can include apiezoelectric actuator layer that is provided on the first or secondoptical cladding layer. The piezoelectric actuator layer can beconfigured to expand or contract in response to an applied electricfield. For example, the piezoelectric actuator layer can be a thin filmformed from a piezoelectric material, including, but not limited to,AlN, GaN, ZnO and ZnS. In response to the applied electric field, thedeflection angle of the at least one of the first and secondout-of-plane waveguide portions can be adjusted. In addition, the angleof optical polarization rotation between input and output light is afunction of the deflection angle, and therefore, by adjusting thedeflection angle it is possible to adjust the angle of opticalpolarization rotation.

Alternatively or additionally, the core and optical cladding materiallayers constituting the waveguide portions can be formed from anymaterial that allows the waveguide to guide light including, but notlimited to, semiconductors (e.g., Group III-V or Group II-VIsemiconductor materials), polymers, amorphous glasses, chalocogenides,etc. Optionally, the core material layer can be formed from silicon(Si). Alternatively or additionally, the first optical cladding layercan be formed from plasma enhanced chemical vapor deposition (“PECVD”)silica (SiO₂) or buried oxide (“BOX”) SiO₂. Additionally, the secondoptical cladding layer can be formed from the other of PECVD SiO₂ or BOXSiO₂.

An example photonic integrated circuit (PIC) chip can include asubstantially planar substrate, electronic and photonic circuitry formedon the substantially planar substrate, and an optical polarizationcontroller formed on the substantially planar substrate and electricallyand photonically coupled to the electronic and photonic circuitry. Theoptical polarization controller can include a waveguide unit cell, andthe waveguide unit cell can include a first out-of-plane waveguideportion and a second out-of-plane waveguide portion coupled to the firstout-of-plane waveguide portion. Each of the first and secondout-of-plane waveguide portions can respectively include a core materiallayer arranged between a first optical cladding layer having a firststress-response property and a second optical cladding layer having asecond stress-response property. The first and second stress-responseproperties can be different such that each of the first and secondout-of-plane waveguide portions is deflected by a deflection angle.

Additionally, the first out-of-plane waveguide portion can be deflectedtoward or away from the substantially planar substrate. Additionally,the second out-of-plane waveguide portion can be deflected toward oraway from the substantially planar substrate.

Alternatively or additionally, an angle of optical polarization rotationbetween input and output light can be a function of the deflectionangle.

Optionally, the optical polarization controller can include a pluralityof waveguide unit cells coupled in series and formed on thesubstantially planar substrate. Additionally, an angle of opticalpolarization rotation between input and output light can be a functionof a number of the waveguide unit cells and the deflection angle.Additionally, the optical polarization controller can include one ormore in-plane waveguide portions. For example, each respective in-planewaveguide portion can be coupled between two waveguide unit cells.

Alternatively or additionally, the deflection angle of at least one ofthe first and second out-of-plane waveguide portions can be configuredto be adjustable in response to at least one of an electrical,mechanical, thermal and optical excitation. For example, at least one ofthe first and second out-of-plane waveguide portions can include apiezoelectric actuator layer that is provided on the first or secondoptical cladding layer. The piezoelectric actuator layer can beconfigured to expand or contract in response to an applied electricfield. For example, the piezoelectric actuator layer can be a thin filmformed from a piezoelectric material, including, but not limited to,AlN, GaN, ZnO and ZnS. In response to the applied electric field, thedeflection angle of the at least one of the first and secondout-of-plane waveguide portions can be adjusted. In addition, the angleof optical polarization rotation between input and output light is afunction of the deflection angle, and therefore, by adjusting thedeflection angle it is possible to adjust the angle of opticalpolarization rotation.

Alternatively or additionally, the core and optical cladding materiallayers constituting the waveguide portions can be formed from anymaterial that allows the waveguide to guide light including, but notlimited to, semiconductors (e.g., Group III-V or Group II-VIsemiconductor materials), polymers, amorphous glasses, chalocogenides,etc. Optionally, the core material layer can be formed from Si.Alternatively or additionally, the first optical cladding layer can beformed from PECVD SiO₂ or BOX SiO₂. Additionally, the second opticalcladding layer can be formed from the other of PECVD SiO₂ or BOX SiO₂.

Optionally, the electronic and photonic circuitry can be based on CMOScircuitry.

Another example optical polarization controller can include asubstantially planar substrate, a bus waveguide formed on thesubstantially planar substrate, a microring waveguide formed on thesubstantially planar substrate and optically coupled to the buswaveguide, and a coupling controller that is configured to adjust anamount of optical coupling between the bus waveguide and the microringwaveguide. The microring waveguide can include an out-of-plane waveguideportion having a core material layer arranged between a first opticalcladding layer having a first stress-response property and a secondoptical cladding layer having a second stress-response property. Thefirst and second stress-response properties can be different such thatthe out-of-plane waveguide portion is deflected by a deflection angle.

Optionally, the out-of-plane waveguide portion can further include afirst out-of-plane waveguide portion and a second out-of-plane waveguideportion coupled to the first out-of-plane waveguide portion. Each of thefirst and second out-of-plane waveguide portions can respectivelyinclude a core material layer arranged between a first optical claddinglayer having a first stress-response property and a second opticalcladding layer having a second stress-response property. The first andsecond stress-response properties can be different such that each of thefirst and second out-of-plane waveguide portions is deflected by adeflection angle.

Additionally, the first out-of-plane waveguide portion can be deflectedtoward or away from the substantially planar substrate. Additionally,the second out-of-plane waveguide portion can be deflected toward oraway from the substantially planar substrate.

Alternatively or additionally, the microring waveguide can furtherinclude an in-plane waveguide portion connected between terminal ends ofthe out-of-plane waveguide portion.

Alternatively or additionally, an angle of optical polarization rotationbetween input and output light can be a function of the coupling betweenthe bus waveguide and the microring waveguide. Alternatively oradditionally, an angle of optical polarization rotation between inputand output light can be a function of an effective path length of themicroring waveguide.

Optionally, the coupling controller can be configured to adjust theamount of optical coupling between the bus waveguide and the microringwaveguide by at least one of an electrical, mechanical, thermal andoptical excitation. For example, the coupling controller can becontrolled by a micro-heater. The micro-heater can be configured toadjust the amount of optical coupling between the bus waveguide and themicroring waveguide by adjusting a temperature of the bus waveguide. Itshould be understood that the temperature of the bus waveguide isrelated to a refractive index of the bus waveguide, which effects theamount of optical coupling between the bus waveguide and the microringwaveguide. Alternatively or additionally, the coupling controller can becontrolled by at least one of a PIN junction, a PN junction, and ametal-oxide-silicon (“MOS”) capacitor. The PIN junction, PN junction, orMOS capacitor can be configured to adjust the amount of optical couplingbetween the bus waveguide and the microring waveguide by carrierinjection, depletion, or accumulation. It should be understood that theamount of carriers is related to the refractive index and absorption ofthe bus waveguide, which effects the amount of optical coupling betweenthe bus waveguide and the microring waveguide.

Alternatively or additionally, the core and optical cladding materiallayers constituting the out-of-plane waveguide portion can be formedfrom any material that allows the waveguide to guide light including,but not limited to, semiconductors (e.g., Group III-V or Group II-VIsemiconductor materials), polymers, amorphous glasses, chalocogenides,etc. Optionally, the core material layer can be formed from Si.Alternatively or additionally, the first optical cladding layer can beformed from PECVD SiO₂ or BOX SiO₂. Additionally, the second opticalcladding layer can be formed from the other of PECVD SiO₂ or BOX SiO₂.

Another example PIC chip can include a substantially planar substrate,electronic and photonic circuitry formed on the substantially planarsubstrate, and an optical polarization controller formed on thesubstantially planar substrate and electrically and photonically coupledto the electronic and photonic circuitry. The optical polarizationcontroller can include a bus waveguide, a microring waveguide opticallycoupled to the bus waveguide, and a coupling controller that isconfigured to adjust an amount of optical coupling between the buswaveguide and the microring waveguide. The microring waveguide caninclude an out-of-plane waveguide portion having a core material layerarranged between a first optical cladding layer having a firststress-response property and a second optical cladding layer having asecond stress-response property. The first and second stress-responseproperties can be different such that the out-of-plane waveguide portionis deflected by a deflection angle.

Optionally, the out-of-plane waveguide portion can further include afirst out-of-plane waveguide portion and a second out-of-plane waveguideportion coupled to the first out-of-plane waveguide portion. Each of thefirst and second out-of-plane waveguide portions can respectivelyinclude a core material layer arranged between a first optical claddinglayer having a first stress-response property and a second opticalcladding layer having a second stress-response property. The first andsecond stress-response properties can be different such that each of thefirst and second out-of-plane waveguide portions is deflected by adeflection angle.

Additionally, the first out-of-plane waveguide portion can be deflectedtoward or away from the substantially planar substrate. Additionally,the second out-of-plane waveguide portion can be deflected toward oraway from the substantially planar substrate.

Alternatively or additionally, the microring waveguide can furtherinclude an in-plane waveguide portion connected between terminal ends ofthe out-of-plane waveguide portion.

Alternatively or additionally, an angle of optical polarization rotationbetween input and output light can be a function of the coupling betweenthe bus waveguide and the microring waveguide. Alternatively oradditionally, an angle of optical polarization rotation between inputand output light can be a function of an effective path length of themicroring waveguide.

Optionally, the coupling controller can be configured to adjust theamount of optical coupling between the bus waveguide and the microringwaveguide by at least one of an electrical, mechanical, thermal andoptical excitation. For example, the coupling controller can becontrolled by a micro-heater. The micro-heater can be configured toadjust the amount of optical coupling between the bus waveguide and themicroring waveguide by adjusting a temperature of the bus waveguide. Itshould be understood that the temperature of the bus waveguide isrelated to a refractive index of the bus waveguide, which effects theamount of optical coupling between the bus waveguide and the microringwaveguide. Alternatively or additionally, the coupling controller can becontrolled by at least one of a PIN junction, a PN junction, and a MOScapacitor. The PIN junction, PN junction, or MOS capacitor can beconfigured to adjust the amount of optical coupling between the buswaveguide and the microring waveguide by carrier injection, depletion,or accumulation. It should be understood that the amount of carriers isrelated to the refractive index and absorption of the bus waveguide,which effects the amount of optical coupling between the bus waveguideand the microring waveguide

Alternatively or additionally, the core and optical cladding materiallayers constituting the out-of-plane waveguide portion can be formedfrom any material that allows the waveguide to guide light including,but not limited to, semiconductors (e.g., Group III-V or Group II-VIsemiconductor materials), polymers, amorphous glasses, chalocogenides,etc. Optionally, the core material layer can be formed from Si.Alternatively or additionally, the first optical cladding layer can beformed from PECVD SiO₂ or BOX SiO₂. Additionally, the second opticalcladding layer can be formed from the other of PECVD SiO₂ or BOX SiO₂.

Optionally, the electronic and photonic circuitry can be based on CMOScircuitry.

Other systems, methods, features and/or advantages will be or may becomeapparent to one with skill in the art upon examination of the followingdrawings and detailed description. It is intended that all suchadditional systems, methods, features and/or advantages be includedwithin this description and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The components in the drawings are not necessarily to scale relative toeach other. Like reference numerals designate corresponding partsthroughout the several views.

FIG. 1A is a diagram illustrating one complete turn of a helically woundoptical fiber (“the helix”) in physical space. FIG. 1B is a diagramillustrating a closed curve traced out by light momentum in momentumspace for one complete turn of the helix in physical space. The solidangle subtended by the shaded portion in FIG. 1B corresponds to themagnitude of the Berry's phase, which manifests as a polarizationrotation.

FIG. 2A is a schematic diagram of an example optical polarizationcontroller (also referred to herein as a “polarization rotator”) inphysical space. FIG. 2B is a diagram illustrating light travelingthrough the optical polarization controller shown in FIG. 2A in momentumspace. The non-zero solid angle subtended by the shaded surface in FIG.2B corresponds to non-zero Berry's phase, which manifests as apolarization rotation.

FIG. 3A is a diagram illustrating an in-plane optical waveguide. FIG. 3Bis a diagram illustrating an example out-of-plane optical waveguide.FIG. 3C illustrates that the optical mode is highly confined to thewaveguide core so the oxide-air boundary is insignificant.

FIG. 4A is a schematic diagram illustrating an optical polarizationcontroller having a plurality of waveguide unit cells. FIG. 4B is ascanning electron micrograph (“SEM”) of a waveguide unit cell showing apitch angle of θ=9°. FIG. 4C is a graph illustrating predictedpolarization rotation due to Berry's phase and corresponding powertransmission versus a number of waveguide unit cells. In FIG. 4C, it isassumed that optical power with linear polarization is injected at theinput, a linear polarizer is used at the output before photodetection,and 1 dB loss for N=8 waveguide unit cells.

FIG. 5 is a diagram illustrating an example out-of-plane opticalwaveguide having a piezoelectric actuator layer for voltage control ofangular deflection.

FIGS. 6A-6F is a set of drawings illustrating an example method offabricating an out-of-plane optical waveguide.

FIG. 7 is a diagram illustrating a waveguide used for finite-elementmethod (“FEM”) simulation.

FIGS. 8A-8D are contour maps of electric fields at the input and outputof the simulated silicon waveguide, with 300 nm×300 nm cross-section,shown in FIG. 7. The designed polarization rotation angle is 60°. Inparticular, FIG. 8A illustrates the contour map of E_(x) at the input ofthe waveguide, FIG. 8B illustrates the contour map of E_(y) at the inputof the waveguide, FIG. 8C illustrates the contour map of E_(x) at theoutput of the waveguide, and FIG. 8D illustrates the contour map ofE_(y) at the output of the waveguide.

FIG. 9 is a graph illustrating simulated polarization rotation angles atbending radius equal to 5 μm, 10 μm, and 20 μm, and extracted usingE_(x) and E_(y) components, plotted versus theory prediction.

FIG. 10A is a schematic diagram of an optical polarization controllerusing a microring configuration. FIG. 10B is a top-down opticalmicrograph of the optical polarization controller shown in FIG. 10A.FIG. 10C is an optical interferometric surface profilometry measurementof the microring shown in FIG. 10B showing an out-of-plane deflection of1 μm.

FIGS. 11A-11C are graphs illustrating measured optical transmission forthe output TE polarization and the output TM polarization of the opticalpolarization controller shown in FIG. 10A. The input polarization is TE.FIG. 11A illustrates 0 V DC bias, FIG. 11B illustrates 4 V DC bias, andFIG. 11C illustrates 8 V DC bias. The resonance wavelength exhibits aslight redshift with tuning power due to the proximity of themicroheater to the microring. Comparing FIGS. 11B and 11C, theconversion loss is 1.4 dB.

DETAILED DESCRIPTION

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art. Methods and materials similar or equivalent to those describedherein can be used in the practice or testing of the present disclosure.As used in the specification, and in the appended claims, the singularforms “a,” “an,” “the” include plural referents unless the contextclearly dictates otherwise. The term “comprising” and variations thereofas used herein is used synonymously with the term “including” andvariations thereof and are open, non-limiting terms. The terms“optional” or “optionally” used herein mean that the subsequentlydescribed feature, event or circumstance may or may not occur, and thatthe description includes instances where said feature, event orcircumstance occurs and instances where it does not. Whileimplementations will be described for on-chip optical polarizationcontrollers, it will become evident to those skilled in the art that theimplementations are not limited thereto.

As described above, broadband and tunable polarization rotators forpolarization transparent PICS are provided herein. An examplepolarization rotator is based on a physical phenomena referred to asBerry's phase. Berry's phase is a quantum-mechanical phenomenon that maybe observed at the macroscopic optical level through the use of anenormous number of photons in a single coherent state. A. Tomita and R.Y. Chiao, “Observation of Berry's topological phase by use of an opticalfiber,” Physical Review Letters 57, 937-940 (1986). According to quantumtheory, the state of a particle at any given time is described by acomplex wave function Ψ. If the system evolves adiabatically and thenreturns to its original condition, the final wave function Ψ′ is relatedto the original wave function Ψ by Ψ′=Ψexp(iφ). The additional phase φacquired by the system depends on a dynamic phase, whose value dependson time, and a geometric phase (i.e., Berry's phase), whose valuedepends on topology. M. V. Berry, “Quantal phase factors accompanyingadiabatic changes,” Proceedings of the Royal Society of London. SeriesA, Mathematical and Physical Sciences 392, 45-57 (1984). P.Senthilkumaran et al., “Fiber-optic Sagnac interferometer for theobservation of Berry's topological phase,” Journal of the OpticalSociety of America B 17, 1914-1919 (2000).

A direct macroscopic measurement of Berry's phase may be obtainedthrough an observation of the polarization rotation of plane-polarizedlight when it is transported along a closed path in momentum space. Fewexperiments on the manifestations of Berry's phase for photons have beenreported, and those that have been can be divided into those that useoptical fiber and those that use discrete optical components. R. Y.Chiao and Y. S. Wu, “Manifestations of Berry's topological phase for thephoton,” Physical Review Letters 57, 933-936 (1986). A. Tomita and R. Y.Chiao, “Observation of Berry's topological phase by use of an opticalfiber,” Physical Review Letters 57, 937-940 (1986). K. Y. Bliokh et al.,“Geometrodynamics of spinning light,” Nature Photonics 2, 748-753(2008). Single-mode optical fiber is a particularly useful medium forcontrolling the direction of momentum of light along its path lengthsince the momentum vector is always parallel to the axis of the fiber.The angle of rotation of the polarized light does not come from a localelasto-optic effect caused by torsional stress in the fiber.Furthermore, the effect is independent of the detailed materialproperties of the fiber. The rotation angle arises only from the overallgeometry of the path taken by the light. It is a global topologicaleffect. A. Tomita and R. Y. Chiao, “Observation of Berry's topologicalphase by use of an optical fiber,” Physical Review Letters 57, 937-940(1986).

In the special case of planar (e.g., non-helical) paths, such as thepaths typically taken by planar optical waveguides (e.g., opticalwaveguides fabricated on PICs), no significant optical rotation isobserved independent of the complexity of the path. A. Tomita and R. Y.Chiao, “Observation of Berry's topological phase by use of an opticalfiber,” Physical Review Letters 57, 937-940 (1986). In other words,light is able to distinguish whether it is propagating in two or threespatial dimensions. In order to manifest Berry's phase in planar opticalwaveguides (e.g., optical waveguides fabricated on PICs), out-of-planethree-dimensional waveguides can be introduced to create atwo-dimensional momentum-space with non-zero (Gaussian) curvature. Owingto its geometric origin, Berry's phase has universality in many fieldsof science. Berry's phase is referred to as the topological phase,geometric phase, or Pancharatnam-Berry phase. S. Pancharatnam,“Generalized Theory of Interference, and Its Applications. Part I.Coherent Pencils”. Proceedings Indian Academy of Science A 44, 247-262(1956). In classical mechanics, the Hannay angle is the analogue of theBerry phase. J. Hannay, “Angle variable holonomy in adiabatic excursionof an integrable Hamiltonian,” Journal of Physics A 18, 221-230 (1985).The most widely known mechanical manifestation of Berry's phase is theFoucault pendulum. M. Foucault, “Physical demonstration of the rotationof the earth by means of the pendulum,” Journal of the FranklinInstitute 51, 350-353 (1851).

Berry's phase has been observed in helically wound optical fibers. A.Tomita and R. Y. Chiao, “Observation of Berry's topological phase by useof an optical fiber,” Physical Review Letters 57, 937-940 (1986). Asdescribed in detail below, Berry's phase can also be exploited in planaroptical waveguides (e.g., optical waveguides fabricated on PICs). Thepropagation vector of light traveling in a single-mode fiber isconstrained to be parallel to the local fiber axis. Thus, when a fiber102 is wound into a helical path in physical-space as shown in FIG. 1A,the direction of momentum of light continuously changes in a way thatcan be represented on a momentum-space sphere as shown in FIG. 1B.Monochromatic light at wavelength 2 carries a momentum given byp={circumflex over (x)}p_(x)+ŷp_(y)+{circumflex over (z)}p_(z)=ℏk, wherek is the propagation vector with magnitude 2π/λ and ℏ is Planck'sconstant divided by 2π. Referring to FIG. 1A, the ends 102A, 102B of thehelically wound part of the fiber loop are arranged to lie along thesame axis 104, so that the light travels through a closed path inmomentum-space (e.g., the closed curve 106 shown in FIG. 1B). Referringnow to FIG. 1B, the magnitude of the rotation of polarization is equalto the magnitude of the Berry's phase, which is equal to the solid anglesubtended by the shaded area 110 at the center of the momentum-spacesphere. Variations in the helical geometry results in variations inBerry's phase. F. Wassmann and A. Ankiewicz, “Berry's phase analysis ofpolarization rotation in helicoidal fibers,” Applied Optics 37,3902-3911 (1998). A change in wavelength of the light results in achange of the radius of the sphere in momentum-space but not the solidangle. Therefore, the effect is intrinsically broadband.

A necessary condition for the existence of non-trivial Berry's phase isthat the system possesses a momentum space with non-zero subtended solidangle. In the vernacular of differential geometry, a system must possessa phase space with non-zero Gaussian curvature to observe Berry's phase.It should be understood that in-plane optical waveguides (or planaroptical waveguides) possess zero Gaussian curvature, and therefore, donot observe Berry's phase. In order to observe Berry's phase, at least aportion of the planar optical waveguides can be deflected out-of-plane,which is described in detail below.

Referring now to FIG. 2A, a schematic diagram of an example opticalpolarization controller 200 (also referred to herein as a “polarizationrotator”) in physical space is shown. The optical polarizationcontroller 200 can include a substantially planar substrate 202 and awaveguide unit cell (described below) formed on the substantially planarsubstrate 202. Light, for example emitted by a light source such as alaser, a light emitting diode, etc., can be input into the opticalpolarization controller 200 at coupling point 201A. The light can beoutput from the optical polarization controller 200 at coupling point201B. Optionally, the light can be input/output to/from the opticalpolarization controller 200 through cantilever couplers, which aredescribed in detail in U.S. Pat. No. 8,442,368 to Reano et al., entitled“Cantilever Couplers for Intra-Chip Coupling to Photonic IntegratedCircuits.” Optionally, the substantially planar substrate 202 can bebased on a Si substrate. Although Si is provided as an example materialfor the substantially planar substrate 202, it can optionally be formedof other materials including, but not limited to, semiconductors,polymers, amorphous glasses, chalcogenides, and electro-opticalcrystals. The substantially planar substrate 202 can optionally be a PICchip. It should be understood that a PIC chip can be a device thatincorporates electronic and photonic circuitry. As used herein, photoniccircuitry performs functions based on the physics of photons, andelectronic circuitry performs functions based on the physics ofelectrons.

The waveguide unit cell can include a first out-of-plane waveguideportion 204A and a second out-of-plane waveguide portion 204B coupled tothe first out-of-plane waveguide portion 204A. Although a singlewaveguide unit cell is shown in FIG. 2A, it is possible to provide anoptical polarization controller having a plurality of waveguide unitcells (described below). The first out-of-plane waveguide portion 204Acan be deflected either vertically up or down, and the secondout-of-plane waveguide portion 204B can be deflected the oppositedirection as the first out-of-plane waveguide portion 204A, e.g., eithervertically down or up. As shown in FIG. 2A, the first out-of-planewaveguide portion 204A (i.e., the dotted line) forms a 180° bend andascends from a minimum height (e.g., the substantially planar substrate202) to a maximum height (e.g., spaced away from the substantiallyplanar substrate 202). It should be understood that the firstout-of-plane waveguide portion 204A can form a bend of more or less than180°, which is provided only as an example. In other words, the firstout-of-plane waveguide portion 204A is deflected away from thesubstantially planar substrate 202, for example, by a deflection angle(described below). The light traveling through the first out-of-planewaveguide portion 204A in the momentum space is shown by the dotted linein FIG. 2B. As shown in FIG. 2A, the second out-of-plane waveguideportion 204B (i.e., the dashed-dotted line) descends from the maximumheight (e.g., where it is coupled to the first out-of-plane waveguideportion 204A) to the minimum height (e.g., the substantially planarsubstrate 202). In other words, the second out-of-plane waveguideportion 204B is deflected toward the substantially planar substrate 202,for example, by the deflection angle (described below). The lighttraveling through the second out-of-plane waveguide portion 204B in themomentum space is shown by the dashed-dotted line in FIG. 2B. As shownin FIG. 2A, the optical polarization controller 200 can also include anin-plane waveguide portion 206 (i.e., the solid line), for example,which is coupled to the second out-of-plane waveguide portion 204B. Asused herein, an in-plane waveguide portion is a not-out-of-planewaveguide portion (i.e., it is not deflected away from/toward thesubstantially planar substrate 202). As shown in FIG. 2B, the in-planewaveguide portion 206 forms a 180° bend and remains in-plane with thesubstantially planar substrate 202. It should be understood that thein-plane waveguide portion 206 can form a bend of more or less than180°, which is provided only as an example. The light traveling throughthe in-plane waveguide portion 206 in the momentum space is shown by thesolid line in FIG. 2B. Light propagation along this three-dimensionalconfiguration in physical space (i.e., through the first out-of-planewaveguide portion 204A, the second out-of-plane waveguide portion 204Band the in-plane waveguide portion 206 shown in FIG. 2A) results in anon-zero subtended solid angle in momentum space, which is shown as theshaded area 210 in FIG. 2B. Therefore, the optical polarizationcontroller 200 exhibits Berry's phase. As described above, a change inwavelength results in a change of the radius of the sphere in momentumspace shown in FIG. 2B, but not a change in the solid angle. Therefore,the effect is intrinsically broadband.

Referring again to FIG. 2B, θ denotes the angle of ascent/descent (ordeflection) of the first out-of-plane waveguide portion 204A/the secondout-of-plane waveguide portion 204B in the physical space shown in FIG.2A. The output light (e.g., the light output at coupling point 201B)appears with polarization rotation equal to 2θ (e.g., as compared to thelight input at coupling point 201A) due to Berry's phase because themagnitude of the solid angle extended by the shaded area 210 in momentumspace shown in FIG. 2B is 2θ. In other words, an angle of opticalpolarization rotation between input and output light can be a functionof the deflection angle (e.g., angle of polarization rotation=2θ, whereθ is the deflection angle). Additionally, and as described below withregard to FIGS. 4A-4C, a series concatenation of N waveguide unit cells(e.g., a plurality of waveguide unit cells described with regard toFIGS. 2A-2B) produces a polarization rotation of 2Nθ. In other words, anangle of optical polarization rotation between input and output lightcan be a function of a number of waveguide unit cells and the deflectionangle (e.g., angle of polarization rotation=2Nθ, where N is the numberof waveguide unit cells and θ is the deflection angle). Further, foroptical power with linear polarization injected at the input, thepresence of a linear polarizer at the output yields a prediction for thefunctional form of the output power that is proportional to cos² (2Nθ).

Referring now to FIGS. 3A-3B, example optical waveguides are shown. Inparticular, FIG. 3A is a diagram illustrating an in-plane opticalwaveguide. The in-plane optical waveguide is formed on a substantiallyplanar substrate 302A and includes a core material layer 301A arrangedbetween a first optical cladding layer 303A and a second opticalcladding layer 305A. In contrast, FIG. 3B is a diagram illustrating anexample out-of-plane optical waveguide 304. In order to deflect opticalwaveguides out-of-plane, bilayer thin film stress between top and bottomoptical cladding layers of free-standing silicon strip waveguides can beexploited. For example, a silicon waveguide core can be embedded withinan oxide thin film bilayer cladding that deflects out-of-plane becauseof residual stress. Accordingly, each of the first and secondout-of-plane optical waveguide portions 204A, 204B shown in FIG. 2A(described with regard to FIG. 3B as an “out-of-plane optical waveguide304”) can be deflected out-of-plane (e.g., either vertically up or downwith respect to a plane) by exploiting bilayer thin film stress betweenthe optical cladding layers. The out-of-plane optical waveguide 304 canbe formed on a substantially planar substrate 302B, e.g., asubstantially planar Si substrate. Although Si is provided as an examplematerial for the substantially planar substrate 302B, it can optionallybe formed of other materials including, but not limited to,semiconductors, polymers, amorphous glasses, chalcogenides, andelectro-optical crystals. The out-of-plane optical waveguide 304 caninclude a core material layer 301B arranged between a first opticalcladding layer 303B having a first stress-response property and a secondoptical cladding layer 305B having a second stress-response property.The first and second stress-response properties can be different suchthat the out-of-plane optical waveguide 304 is deflected out-of-plane bya deflection angle. The first and second optical cladding layers 303Band 305B are also referred to herein as the “bilayer optical cladding.”The out-of-plane deflection of the out-of-plane optical waveguide 304relies on the thin film stress that arises naturally from thin filmdeposition. The sum of mean and gradient stresses results in aspontaneous out-of-plane deflection when the out-of-plane opticalwaveguide 304 is released from the substantially planar substrate 302B.P. Sun and R. M. Reano, “Cantilever couplers for intra-chip coupling tosilicon photonic integrated circuits,” Optics Express 17, 4565-4574(2009). The core material layer can be formed from any material thatallows the waveguide to guide light including, but not limited to,semiconductors (e.g., Group III-V or Group II-VI semiconductormaterials), polymers, amorphous glasses, chalocogenides, etc.Optionally, the core material layer can be formed from Si. Optionally,the first optical cladding layer 303B is PECVD silica or BOX silica, andthe second optical cladding layer 305B is the other of BOX silica orPECVD silica. For example, in FIG. 3B, the first optical cladding layer303B can be BOX silica and the second optical cladding layer 305B can bePECVD silica. Although PECVD silica and BOX silica are provided asexample materials for the first and second optical cladding layers 303Band 305B, this disclosure contemplates using other materials withdifferent stress-response properties as the bilayer optical cladding. Asshown in FIG. 3C, numerical analysis of the electromagnetic mode,indicated by the magnitude of the x-component of the optical electricfield, |E_(x)|, shows high confinement to the waveguide core (e.g., thecore material layer 301B in FIG. 3B) at telecommunications wavelengthsso the oxide air boundary is insignificant.

Referring to FIG. 4A, a schematic diagram illustrating an opticalpolarization controller 400 having a plurality of waveguide unit cells402 is shown. The optical polarization controller 400 can include asubstantially planar substrate 202 and a plurality of waveguide unitcells 402 formed on the substantially planar substrate 202. Inparticular, a series concatenation of eight waveguide unit cells 402(N=8) is shown in FIG. 4A. In other words, the optical polarizationcontroller 400 can include a plurality of waveguide unit cells 402coupled in series and formed on the substantially planar substrate 202.Although eight waveguide unit cells are provided as an example herein,this disclosure contemplates using any number of waveguide unit cells(e.g., more or less than 8) in the optical polarization controller 400.Similar to FIG. 2A, the optical polarization controller 400 shown inFIG. 4A can include a coupling point 201A for inputting light and acoupling point 201B for outputting light. For example, the light canoptionally be input/output to/from the optical polarization controller400 through cantilever couplers, which are described in detail in U.S.Pat. No. 8,442,368 to Reano et al., entitled “Cantilever Couplers forIntra-Chip Coupling to Photonic Integrated Circuits.”

Each of the waveguide unit cells 402 can include a first out-of-planewaveguide portion 204A and a second out-of-plane waveguide portion 204B,which is coupled to the first out-of-plane waveguide portion 204A. Thewaveguide unit cells can be defined by electron beam lithography andreleased by plasma etching, as described above with regard to FIG. 3B,for example. P. Sun and R. M. Reano, “Cantilever couplers for intra-chipcoupling to silicon photonic integrated circuits,” Optics Express 17,4565-4574 (2009). Alternatively, the waveguide unit cells 402 can bedefined by other microfabrication lithography techniques including, butnot limited to, photolithography and nanoimprint lithography andreleased by other microfabrication patterning techniques including, butnot limited to, wet, dry, and particle beam etching. The first andsecond out-of-plane waveguide portions 204A and 204B are described indetail above and are therefore not described in further detail below.Additionally, as shown in FIG. 4A, the optical polarization controllercan include one or more in-plane waveguide portions 206, which are alsodescribed in detail above and are therefore not described in furtherdetail below. Each respective in-plane waveguide portion 206 can beconnected between two waveguide unit cells 402, as shown in FIG. 4A.

Referring now to FIG. 4B, a scanning electron micrograph (“SEM”) of awaveguide unit cell (e.g., one of the waveguide unit cells 402 shown inFIG. 4A) is shown. In particular, FIG. 4B shows a pitch (i.e.,deflection) angle 404 of the waveguide with respect to the chip surface(e.g., the substantially planar substrate 202 shown in FIG. 4A) of θ=9°.It should be understood that the pitch angle of θ=9° is provided only asan example and that other pitch angles more or less than θ=9° can beachieved. An angle of optical polarization rotation between input andoutput light can be a function of a number of the waveguide unit cellsand the deflection angle (e.g., angle of polarization rotation=2Nθ,where N is the number of waveguide unit cells and θ is the deflection(i.e., pitch) angle). For example, given θ=9°, the polarization rotationdue to Berry's phase and normalized output power versus N waveguide unitcells is shown in FIG. 4C. This disclosure contemplates that circuitlayouts and/or fabrication processes can be used to maximize the pitchangle, θ, in order to minimize the total number of waveguide unit cellsthat are required. In addition, the bandwidth at telecommunicationswavelengths is extraordinary, and possibly, limited only by thewavelength range such that the waveguide remains single mode for TE andTM polarizations.

The deflection angle of an out-of plane waveguide (e.g., the firstand/or second out-of-plane waveguide portions 204A, 204B shown in FIG.2A) can be configured to be adjustable in response to at least one of anelectrical, mechanical, thermal and optical excitation. For example, theamount of deflection can be adjusted mechanically, for example, byturning a screw that applies pressure to the out-of-plane waveguide.Alternatively or additionally, the amount of deflection can be adjustedthermally, for example, by fabricating a layer of metal cladding overthe out-of-plane waveguide and applying a voltage thereto. This causes acurrent to flow in the metal cladding, and due to stress caused by thedifferent thermal expansion coefficients of the metal cladding and theout-of-plane waveguide (e.g., optical cladding layers), the amount ofdeflection can be controlled. Alternatively or additionally, the amountof deflection can be adjusted optically, for example, by shining a lighton the out-of-plane waveguide, which causes its temperature to change.Referring now to FIG. 5, a diagram illustrating an example out-of-planeoptical waveguide 502 having a piezoelectric actuator layer for voltagecontrol of angular deflection is shown. The out-of-plane opticalwaveguide 502 is similar to the out-of-plane optical waveguide 304 shownin FIG. 3B. For example, the out-of-plane optical waveguide 502 can beformed on a substantially planar substrate 302B. Additionally, theout-of-plane optical waveguide 502 can include a core material layer301B arranged between a first optical cladding layer 303B having a firststress-response property and a second optical cladding layer 305B havinga second stress-response property. The first and second stress-responseproperties can be different such that the out-of-plane optical waveguide502 is deflected out-of-plane by a deflection angle. As described above,the out-of-plane optical waveguide 502 can be the first and/or secondout-of-plane waveguide portions described herein. The substantiallyplanar substrate 302B and the first and second optical cladding layer303B and 305B are described in detail above and are therefore notdescribed in further detail below.

As shown in FIG. 5, a piezoelectric actuator layer 504 (e.g., apiezoelectric thin film) can be provided on the out-of-plane opticalwaveguide 502. The piezoelectric actuator layer 504 can be fabricated ontop of the bilayer optical cladding, for example, on the second opticalcladding layer 305B as shown in FIG. 5. For example, the piezoelectricactuator layer 504 can be a thin film formed from a piezoelectricmaterial including, but not limited to, AlN, GaN, ZnO and ZnS. Thesematerials are attractive because of their low temperature processingtemperatures. S. Wilson et al., “New materials for micro-scale sensorsand actuators: An engineering review,” Material Science and EngineeringR: Reports 56, 1-129 (2007). As an example, AlN thin films can beprepared by magnetron sputtering. Although AlN, GaN, ZnO and ZnS areprovided as example materials, this disclosure contemplates using othermaterials for the piezoelectric actuator layer 504. By controlling thesputtering conditions, the AlN can exhibit (002) orientation on selectmetal layers suitable for electrical actuation. M. Ishihara et al.,“Control of preferential orientation of AlN films prepared by thereactive sputtering method,” Thin Solid Films 316, 152-158 (1998). X.-H.Xu et al., “Morphological properties of AlN piezoelectric thin filmsdeposited by DC reactive magnetron sputtering,” Thin Solid Films 388,62-67 (2001). The sputter conditions in argon include the sputter power,the chamber pressure, the spacing between the Al target and substrate,and the N₂ concentration in the Ar/N₂ mixture. Preferential crystalorientation in the (002) direction can be obtained at smalltarget-substrate spacing, low chamber pressure, moderate power, and N₂concentration of ˜50%. The amount of voltage required per deflectionangle per waveguide length can be predicted given the actuator geometry,film thicknesses, piezoelectric coefficient, and Young's modulus. M. R.Steel et al., “The piezoelectric bimorph: An experimental andtheoretical study of its quasistatic response,” Journal of Physics D:Applied Physics 11, 979-989 (1978). F. Martin, et al., “Thicknessdependence of the properties of highly c-axis textured AlN thin films,”Journal of Vacuum Science and Technology A: Vacuum, Surfaces, and Films22, 361-365 (2004). For example, an AlN film thickness of 250 nm andactuation voltage of 14 V results in a deflection angle of 1 μm for awaveguide length of 200 μm for the out-of-plane optical waveguide 502shown in FIG. 5. Longer waveguide lengths result in lower actuationvoltages.

The piezoelectric actuator layer 504 is incorporated for voltage controlof the amount of deflection of the out-of-plane optical waveguide 502.As described above, the angle of optical polarization rotation betweeninput and output light is a function of the deflection angle, andtherefore, by adjusting the deflection angle of the out-of-plane opticalwaveguide 504, it is possible to adjust the angle of opticalpolarization rotation. In other words, voltage control allows fordynamic tuning of Berry's phase in any optical polarization controllerdescribed herein. For example, when an external electric field isapplied to the piezoelectric actuator layer 504, the piezoelectricactuator layer 504 contracts or expands along the waveguide longitudinaldirection 506 (e.g., the dotted line in FIG. 5). Accordingly, it ispossible to tune the angular deflection of the out-of-plane opticalwaveguide 502. Further, since the electromagnetic mode is highlyconfined to the silicon waveguide (e.g., the core material layer 301B),the optical field is negligibly perturbed by the piezoelectric actuatorlayer 504.

Referring now to FIGS. 6A-6F, a set of drawings illustrating an examplemethod of fabricating an out-of-plane optical waveguide is shown. Thisdisclosure contemplates that the out-of-plane optical waveguidesdescribed herein can be fabricated according to the example process flowdescribed below. Alternatively, the out-of-plane optical waveguides canbe fabricated according to other microfabrication techniques, such aselectron beam lithography and photolithography, and based on otherchemistries and pattern transfer materials. The principle is to releasethe out-of-plane optical waveguide from the substrate so that theoptical waveguide can deflect out-of-plane due to thin film stress. Inthe current example, first, as shown in FIG. 6A, a waveguide core isfabricated on the SOI substrate. Second, as shown is FIG. 6B, a (1.1 μm)layer of PECVD SiO₂ is applied using SiH₄—N₂O chemistry at 200° C.,covering the waveguide core. A 5 nm titanium adhesive layer and a 150 nmnickel mask are then evaporated on top of the PECVD SiO₂ (FIG. 6C). Thepatterns for the out-of-plane waveguide are written directly on theTi/Ni mask by focused Ga+ ion beam (FIB) milling at 30 kV with a nominalmilling depth of 250 nm (FIG. 6D). The metal mask patterns aretransferred to the SiO₂ layer by reactive ion etching (RIE) using SF₆chemistry (FIG. 6E). The schematic shows deflection of the out-of-planeoptical waveguide after ion etching, however, this is merely forillustrative purposes to demonstrate that the out-of-plane opticalwaveguide is released from the bulk Si device, as further deflectionoccurs during later heat curing or annealing. In an exemplaryembodiment, the etch recipe is tuned to etch SiO₂ anisotropically and toetch silicon isotropically with large undercut in order to fully releasethe out-of-plane optical waveguide from the substrate and aiddeflection. As shown, it is clear that the Si waveguide core ispreferably protected from the RIE, as the RIE etches the Si chip andwould also be expected to etch the waveguide. Finally, the Ti/Ni mask isremoved with HNO₃ and HCl solutions (FIG. 6F). In addition, as describedabove with regard to FIG. 5, a piezoelectric actuator layer can befabricated on top of the out-of-plane optical waveguide.

Referring now to FIG. 7, a diagram illustrating a waveguide 700 used forFEM simulation is shown. In the FEM simulations, the silicon waveguide702 is buried in 1-μm-thick silicon dioxide cladding 704, which is inturn surrounded by 1-μm-thick perfectly matched layer (“PML”) 706 toabsorb outgoing scattering waves. The waveguide is excited by TEpolarized light at the input (point 708), and the frequency-domain fullwave solutions are solved at the wavelength of λ=1.55 μm. It is worthnoting that the wavelength parameter λ does not appear in the theory ofgeometric phase, and is only set as required for frequency domainnumerical simulation. The geometric origin of the polarization rotationimplies that such rotation is independent of wavelength.

At the output (point 710), the waveguide mode is a mixture of thequasi-TE and quasi-TM eigenmodes. FIGS. 8A-8D show the contour maps ofsimulated electric fields E_(x) and E_(y) at the input and output of thesilicon waveguide shown in FIG. 7, which is designed to generate apolarization rotation angle equal to 60°. The electric fields at theinput and output are normalized individually, such that the maximumamplitude of the electric fields is equal to 1.

The polarization rotation angle can be extracted by expanding the hybridmode using the fundamental quasi-TE and quasi-TM modes as shown by Eqn.(1).

$\begin{matrix}{{\alpha_{x} = {\tan^{- 1}\left\lbrack \frac{\int{\int{E_{x,{TM}}E_{x}^{*}{{dxdy}/{\int{\int{{E_{x,{TM}}}^{2}{dxdy}}}}}}}}{\int{\int{E_{x,{TE}}E_{x}^{*}{{dxdy}/{\int{\int{{E_{x,{TE}}}^{2}{dxdy}}}}}}}} \right\rbrack}}{\alpha_{y} = {\tan^{- 1}\left\lbrack \frac{\int{\int{E_{y,{TM}}E_{y}^{*}{{dxdy}/{\int{\int{{E_{y,{TM}}}^{2}{dxdy}}}}}}}}{\int{\int{E_{y,{TE}}E_{y}^{*}{{dxdy}/{\int{\int{{E_{y,{TE}}}^{2}{dxdy}}}}}}}} \right\rbrack}}} & (1)\end{matrix}$where E_(x,TE) and E_(y,TE) are the transverse electric fields of the TEeigenmode, E_(x,TM) and E_(y,TM) are the transverse electric fields ofthe TM eigenmode, E_(x) and E_(y) are the transverse electric fields ofthe hybrid mode, α_(x) and α_(y) are the polarization rotation anglesextracted using E_(x) and E_(y), respectively. The polarization rotationangles α_(x) and α_(y) extracted from FEM simulation results are plottedversus the design values at bending radius R=5, 10, and 20 μmrespectively, in FIG. 9.

As shown in FIG. 9, the simulation results are in good agreement withthe theory prediction. The small difference between theory andsimulation can be attributed to discretization error in the waveguidemodel, approximations from the numerical integration of Eqn. (1), andfinite discretization in the finite element method simulation. Nosignificant correlation between the polarization rotation and thebending radius is observed. Simulation results of silicon waveguidesthat have symmetric cross sections but different dimensions, for example250 nm×250 nm, show similar results as that of the 300 nm×300 nmwaveguide.

The polarization rotation based on geometric phase is different from thepolarization rotation induced by birefringence in waveguide bends. Infabricated silicon waveguides, birefringence is inevitably induced byresidual stress, slanted sidewalls, inhomogeneous cladding, and otherfactors. Analysis employing perturbation method and coupled-mode theoryindicates that the TE-TM mode conversion induced by birefringence inwaveguide bends varies with light wavelength, decreases rapidly withbending radius, and approaches zero for symmetric waveguideconfiguration. These characteristics clearly distinguish thepolarization rotation based on geometric phase from that induced bybirefringence in waveguide bends.

Referring now to FIGS. 10A-10C, an optical polarization controller usinga microring configuration is described. Berry's phase for tunablepolarization rotation can be manifested by implementing an out-of-planewaveguide in a microring configuration that realizes a momentum-spacewith non-zero (Gaussian) curvature. In a single round trip of themicroring, the polarization rotates by an angle determined by theout-of-plane deflection. On resonance, the polarization rotation isamplified by the increase in the effective path length. I. Golub,“Berry's phase amplification by a ring resonator”, Opt. Lett. 31,3342-3344 (2006). The overall polarization rotation can be controlledelectrically by tuning the coupling coefficient of a bus waveguidecoupled to the out-of-plane microring. An angle of optical polarizationrotation between input and output light can therefore be a function ofan effective path length of the microring. The example opticalpolarization controller using a microring configuration described hereindemonstrates dynamic tuning between TE and TM modes in silicon stripwaveguides with a 9 dB polarization extinction ratio.

Referring now to FIG. 10A, a schematic diagram of an opticalpolarization controller 1000 using a microring configuration is shown.The optical polarization controller 1000 can include a substantiallyplanar substrate 1002, a bus waveguide 1004 formed on the substantiallyplanar substrate 1002, a microring waveguide 1006 (also referred toherein as a “microring resonator”) formed on the substantially planarsubstrate 1002 and optically coupled to the bus waveguide 1004, and acoupling controller 1008 that is configured to adjust an amount ofoptical coupling between the bus waveguide 1004 and the microringwaveguide 1006. As shown in FIG. 10A, light can be input into the buswaveguide 1004 at coupling point 1001A, and light can be output from thebus waveguide 1004 at coupling point 1001B. Optionally, the light can beinput/output to/from the bus waveguide 1004 through cantilever couplers,which are described in detail in U.S. Pat. No. 8,442,368 to Reano etal., entitled “Cantilever Couplers for Intra-Chip Coupling to PhotonicIntegrated Circuits.” Similar as described above, the substantiallyplanar substrate 1002 can optionally be a Si substrate. For example, thesubstantially planar substrate 1002 can optionally be a PIC chip asdescribed above. In FIG. 10A, the cross-section of the silicon stripwaveguides (i.e., the bus waveguide 1004 and the microring waveguide1006) are 310 nm in width and 300 nm in height. Additionally, the radiusof curvature of the curved section of the microring resonator 1006 is 20μm and the straight sections are 40 μm in length. It should beunderstood, however, that these dimensions are provided only as examplesand that other dimensions can be used.

At least a portion of the microring waveguide 1006 is designed todeflect out-of-plane, for example via thin film stress of the bilayeroptical cladding, such that light propagation along thethree-dimensional configuration in physical space results in a non-zerosubtended solid angle in momentum space. For example, the microringwaveguide 1006 can include a waveguide unit cell 1006A (e.g., the firstand second out-of-plane waveguide portions 204A and 204B described withregard to FIG. 2A) and an in-plane waveguide portion 1006B (e.g., thein-plane waveguide portion 206 described above with regard to FIG. 2A).As described above, the first out-of-plane waveguide portion can bedeflected either vertically up or down, and the second out-of-planewaveguide portion can be deflected the opposite direction as the firstout-of-plane waveguide portion, e.g., either vertically down or up. Asshown in FIG. 10A, the waveguide unit cell 1006A includes a firstout-of-plane waveguide portion that forms a 180° bend and descends froma maximum height (e.g., the substantially planar substrate 1002) to aminimum height (e.g., spaced away from the substantially planarsubstrate 1002). Additionally, as shown in FIG. 10A, the waveguide unitcell 1006A includes a second out-of-plane waveguide portion that ascendsfrom the minimum height (e.g., where it is coupled to the firstout-of-plane waveguide portion) to the maximum height (e.g., thesubstantially planar substrate 1002). In other words, the microringwaveguide 1006 can be formed by coupling the waveguide unit cell 1006Aand the in-plane waveguide portion 1006B to form a microring resonator,for example, by connecting the in-plane waveguide portion 1006B betweenterminal ends of the waveguide unit cell 1006A. Example waveguide unitcells and in-plane waveguide portions are described in detail above andtherefore are not described in further detail below.

Additionally, the microring waveguide 1006 is dual-coupled to the buswaveguide 1004 with the coupling controller 1008 as shown in FIG. 10A.It should be understood that optical coupling between the microringwaveguide 1006 and the bus waveguide 1004 is affect by the distance, thecoupling length and the refractive indices between the microringwaveguide 1006 and the bus waveguide 1004. Optionally, the couplingcontroller 1008 can be configured to adjust the amount of opticalcoupling between the bus waveguide 1004 and the microring waveguide 1006by at least one of an electrical, mechanical, thermal and opticalexcitation. For example, the coupling controller 1008 can be amicro-heater. The micro-heater can be configured to adjust the amount ofoptical coupling between the bus waveguide 1004 and the microringwaveguide 1006 by adjusting a temperature of the bus waveguide 1004. Itshould be understood that the temperature of the bus waveguide 1004 isrelated to a refractive index of the bus waveguide 1004, which effectsthe amount of optical coupling between the bus waveguide 1004 and themicroring waveguide 1006. Alternatively or additionally, the couplingcontroller 1008 can be at least one of a PIN junction, a PN junction,and a MOS capacitor. The PIN junction, PN junction, or MOS capacitor canbe configured to adjust the amount of optical coupling between the buswaveguide 1004 and the microring waveguide 1006 by carrier injection,depletion, or accumulation. It should be understood that the amount ofcarriers is related to the refractive index and absorption of the buswaveguide, which effects the amount of optical coupling between the buswaveguide and the microring waveguide.

Referring to FIG. 10B, a top-down optical micrograph the opticalpolarization controller 1000 shown in FIG. 10A is shown, and referringto FIG. 10C an optical interferometric surface profilometry measurementof the microring 1006 shown in FIG. 10B showing an out-of-planedeflection of 1 μm is shown. The vertical deflection of the microring isobserved to be 1 μm. The polarization rotator (e.g., the opticalpolarization controller 1000 shown in FIG. 10A) can be fabricated in thesilicon-on-insulator material system with 1 μm of buried oxide. Thesilicon waveguides (e.g., the bus waveguide 1004 and the microringwaveguide 1006 shown in FIG. 10A) can be fabricated using electron beamlithography and plasma etching. A top-cladding of PECVD oxide isolatesthe silicon waveguides from the microheater composed of Ti and Al. Asubsequent electron beam lithography step and SF₆ plasma etch areconducted to simultaneously pattern the “J-shape” of the out-of-planemicroring and cantilever couplers for fiber-to-chip light coupling. P.Sun and R. M. Reano, “Cantilever couplers for intra-chip coupling tosilicon photonic integrated circuits”, Opt. Express 17, 4565-4574(2009).

The tunability of the polarization rotation based on Berry's phase ischaracterized by optical transmission measurements. Light from acontinuous wave infrared laser source can be fiber coupled into the chipvia cantilever couplers as described above while the tuning voltage isapplied to the devices through integrated electrodes. An off-chip fiberpolarization controller can be used to produce TE light that is inputinto the chip with a maximum TE/TM polarization extinction ratio,P_(TE)/P_(TM), of 16 dB, where P_(TE) is the optical power in the TEmode and P_(TM) is the optical power in the TM mode. A 10 dB PER on-chippolarization splitter can be used to split the light in the output buswaveguide into a single waveguide TE output port and a single waveguideTM output port. D. Dai and J. E. Bowers, “Novel ultra-short andultra-broadband polarization beam splitter based on a bent directioncoupler,” Opt. Express 19, 18614-18620 (2011). Cantilever couplers asdescribe above can be used to couple the light off chip via opticalfiber where optical power is measured by photodetection.

Referring now to FIGS. 11A-11C, graphs illustrating measured opticaltransmission for the output TE-polarization and the outputTM-polarization of the optical polarization controller shown in FIG. 10Aare shown as a function of wavelength and applied voltage. In FIG. 11A,a resonance for the TM mode in the microring is observed at 1558.2 nmfor a tuning voltage of 0 V. The polarization extinction ratio isobserved to be −6 dB with most of the output power in the TM mode.Increasing the voltage to 4 V results in the measurements shown in FIG.11B. Here, the resonance has red-shifted slightly to 1558.5 nm due tothermal proximity of the microheater. The measured PER has increased toa maximum negative value of −9 dB. FIG. 11C shows the results for the DCbias increased to 8 V. The resonance has shifted again slightly to1558.9 nm due to the microheater. The measured PER is seen to switch to+9 dB, indicating that most of the power resides in the TE mode.Analysis of the structure by coupled mode theory shows that thetransmission response can be characterized by a specific bus-ringcoupling coefficient, denoted y_(θ), that is a function of theout-of-plane deflection angle, denoted θ. Here, the bus-ring couplingcoefficient, denoted y, is controlled experimentally with themicroheater power. When y<y_(θ), the transmission response ischaracterized by a TM resonance peak as observed in FIG. 11A. Wheny=y_(θ), the transmission response is characterized by maximum TM-to-TEpower as shown in FIG. 11B. Finally, when y>y_(θ), the transmissionresponse is characterized by a double peak in the TE power as observedin FIG. 11C. Comparing FIGS. 11B and 11C, the demonstrated conversionloss is 1.4 dB.

Although the subject matter has been described in language specific tostructural features and/or methodological acts, it is to be understoodthat the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described above.Rather, the specific features and acts described above are disclosed asexample forms of implementing the claims.

What is claimed is:
 1. An optical polarization controller, comprising: asubstantially planar substrate; and a waveguide unit cell formed on thesubstantially planar substrate, the waveguide unit cell comprising: afirst out-of-plane waveguide portion, and a second out-of-planewaveguide portion coupled to the first out-of-plane waveguide portion,wherein each of the first and second out-of-plane waveguide portionsrespectively includes a core material layer arranged between a firstoptical cladding layer having a first stress-response property and asecond optical cladding layer having a second stress-response propertythat is different than the first stress-response property such that eachof the first and second out-of-plane waveguide portions is deflected bya deflection angle, wherein the deflection angle of at least one of thefirst out-of-plane waveguide portion or the second out-of-planewaveguide portion is configured to be adjustable in response to anelectrical excitation, and wherein the at least one of the firstout-of-plane waveguide portion or the second out-of-plane waveguideportion further comprises a piezoelectric actuator layer provided on thefirst or second optical cladding layers, the piezoelectric actuatorlayer being configured to expand or contract in response to an appliedelectric field.
 2. The optical polarization controller of claim 1,wherein at least one of the first out-of-plane waveguide portion or thesecond out-of-plane waveguide portion is deflected toward or away fromthe substantially planar substrate.
 3. The optical polarizationcontroller of claim 1, wherein an angle of optical polarization rotationbetween input and output light is a function of the deflection angle. 4.The optical polarization controller of claim 1, further comprising aplurality of waveguide unit cells coupled in series and formed on thesubstantially planar substrate, wherein an angle of optical polarizationrotation between input and output light is a function of a number of thewaveguide unit cells and the deflection angle.
 5. The opticalpolarization controller of claim 4, further comprising one or morein-plane waveguide portions, wherein each respective in-plane waveguideportion is connected between two waveguide unit cells.
 6. The opticalpolarization controller of claim 1, wherein, in response to the appliedelectric field, the deflection angle of the at least one of the firstout-of-plane waveguide portion or the second out-of-plane waveguideportion is adjusted.
 7. The optical polarization controller of claim 1,wherein the piezoelectric actuator layer is a thin film formed from apiezoelectric material.
 8. The optical polarization controller of claim1, wherein: the core material layer is formed from at least one of asemiconductor, a polymer, an amorphous glass, crystal, or achalcogenide, or the first optical cladding layer is formed from atleast one of PECVD SiO₂ or BOX SiO₂, or the second optical claddinglayer is formed from at least one of PECVD SiO₂ or BOX SiO₂.
 9. Anphotonic integrated circuit (PIC) chip, comprising: a substantiallyplanar substrate; electronic and photonic circuitry formed on thesubstantially planar substrate; and the optical polarization controllerof claim 1 formed on the substantially planar substrate and electricallyand photonically coupled to the electronic and photonic circuitry.